The thermal conductivities of silicon and germanium have been determined using the non-stationary hot wire method. Measurements were carried out over the temperature range 293-1724 K on solid and liquid silicon and on liquid germanium in alumina tube. For solid silicon, the thermal conductivities were about 139 W/mK at 293 K and 19 W/mK at 1573 K and displayed temperature dependence steeper than T-1, where T is the temperature. Calculation of thermal conductivities for solid silicon based upon isotope, three-phonon and four-phonon scatterings indicates that phonon conduction dominates heat conduction at temperatures below 1000 K. At temperatures above 1000 K, on the contrary, contributions from electron, hole and electron-hole pair to heat conduction became greater progressively with a temperature rise. For liquid silicon, the thermal conductivity was about 57 W/mK at 1700 K and exhibited a slight increase with an increase in temperature. The thermal conductivity of liquid germanium was about 43 W/mK at 1273 K and slightly increased with increasing temperature. In both liquids, temperature dependency of thermal conductivity values was discussed from the view point of the Wiedemann-Franz law. (C) 2002 Elsevier Science B.V. All rights reserved.